Limits and Continuity (VCE SSCE Mathematical Methods): Flashcards

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Limits and Continuity
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Meaning of limxaf(x)=p\lim_{x \to a} f(x) = p

f(x)f(x) approaches pp as xx approaches aa

Finding limit of polynomial function at a point

Substitute the value directly into the function

Can limit exist if function undefined at that point?

Yes, limit describes behaviour near point, not at it

Limit of a sum

Sum of the limits

Limit of a product

Product of the limits

Limit of quotient (condition?)

Quotient of limits if denominator limit 0\neq 0

When does limxaf(x)\lim_{x \to a} f(x) exist?

When left & right limits exist and are equal

Two conditions for continuity at x=ax=a

f(a)f(a) defined AND limxaf(x)=f(a)\lim_{x \to a}f(x) = f(a)

Which functions are continuous everywhere?

All polynomial functions

Meaning of limxaf(x)\lim_{x \to a^-} f(x)

Limit as xx approaches aa from the left

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